Finn's cycling index






The relative exergy index may be used as a measure for ecosystem integrity and will at least partly cover (1)-(5) of the total of six points given in the definitions by Costanza (1992) (see above).

(1) The homeostasis is embodied in the information of the organisms on how they will meet certain changes by feedback reactions. This information is determined mainly by the genes, which are considered in the calculation of exergy.

(2) Absence of disease is reflected in the biomass, since any ecosystem disease sooner or later will be accompanied by a drop in biomass. As the higher organisms have more genes, exergy will be particularly sensitive to a drop in biomass of these organisms, which is considered as an advantage for the use of exergy as an ecological indicator.

(3) Living matter has higher complexity compared with the same elements in organic form (detritus), which has higher exergy than the elements in inorganic form. Exergy will thereby be a measure of complexity, but not necessarily of diversity. The exergy will generally increase as the ecological niches are better utilised by an increased biodiversity but there are cases, for instance of eutrophication of aquatic ecosystem, where the exergy increases and the biodiversity decreases; see below for further explanation.

(4) Exergy can be shown by the use of statistics on modelling studies to cover a sum of buffer capacities (see below) and is thereby related to the resistance of the ecosystem.

(5) Growth increases in biomass and the genes contain information on how to utilise the resources for growth. The evolution has steadily opened new pathways to utilise the resources (including the ecological niches) better and better. Exergy, which is used for both information and biomass measures, therefore can be considered as the potential for growth. It is interesting in this context that there is a relationship between the exergy stored in the ecosystem and the ability of the system to capture exergy from the solar radiation.

(6) The balance between the system components and the biodiversity are not covered by the use of exergy as integrity indicator because, for instance, eutrophic systems often have a low biodiversity and a biased distribution of the biomass, but a high exergy.

The conclusion from this comparison of Costanza's ecosystem integrity definition and the concept of exergy is that there is a need for supplementary ecosystem integrity indicators. Exergy does not cover all the aspects of ecosystem integrity presented in Costanza's definition.

Specific exergy, ex = Exergy/Volume or Biomass (see Chapter 5) seems to be opposed to the total exergy, Ex, to be a candidate for a better coverage of points 3 and 6 in the definition of ecosystem integrity given above:

(30) Many model studies in this volume and ecological studies (Weiderholm, 1980) clearly show that increased biodiversity means that there is a higher probability of a better utilisation of the available resources, i.e. the value of ex increases. A better utilisation of all ecological niches is accompanied by a higher biodiversity. Thereby the value of ex also measures the structural complexity and the ratio of biomass to total mass (biomass + inorganic matter). A development towards a more complex organism (with more genes) will also result in a higher ex. (60) A better utilisation of all ecological niches means that there will be more species and thereby a better balance between system components, which again may ensure a better balance between various buffer capacities.

Reactions of ecosystems to perturbations have been widely discussed in relation to the stability concepts. However, this discussion has in most cases not considered the enormous complexity of regulation—and feedback mechanisms.

An ecosystem is a soft system that will never return to exactly the same point again. It will attempt to maintain its functions on the highest possible level, but never with exactly the same biological and chemical components in the same concentrations again. The species composition or the food web may or may not have changed, but at least it will not be the same organisms with exactly the same properties. In addition, it is unrealistic to consider that the same combination of forcing functions will occur again. We can observe that an ecosystem has the property of resilience, in the sense that ecosystems have a tendency to recover after stress; but a complete recovery, meaning that exactly the same situation will happen again, will never be realised. The combination of external factors—the impact of the environment on the ecosystem—will never appear again, and even if they would, the internal factors—the components of the ecosystem—would meanwhile have changed and can therefore not react in the same way as the previous internal factors did. Resistance is another widely applied stability concept. It covers the ability of the ecosystem to resist changes when the external factors are changed. An ecosystem will always be changed when the conditions are changed; the question is what exactly is changed and by how much?

It is observed that increased phosphorus loading gives decreased diversity (Ahl and Weiderholm, 1977; Weiderholm, 1980), but eutrophic lakes are highly stable. A similar relationship is obtained between the diversity of the benthic fauna and the phosphorus concentration relative to the depth of the lakes (Weiderholm, 1980); see also Chapter 7.

The concept of buffer capacity (J0rgensen, 1988) has a definition, which allows for a numerical formalisation, for instance in modelling, and it is furthermore applicable to real ecosystems as it acknowledges that some changes will always take place in the ecosystem in response to changed forcing functions. The question is how large these changes are in relation to changes in the conditions (the external variables or forcing functions).

In accordance with the concept the buffer capacity, ¡3, is defined as

¡3 = 1/(8 (state variable)/d (forcing function)) . (2 . 1)

In a multi-dimensional case, when there are n variables xi and m forcing functions fk, i.e. parameters or functions of time describing the impact of the environment on the system, then the buffer capacity is a matrix of (n X m)-dimension:

B = Wpik = 1/(>Xi/»fkII, i = 1,..., n; k = 1, ...m, (2.2)

and we may consider all combinations of state variables and forcing functions. It implies that even for one type of change there are many buffer capacities corresponding to each of the state variables.

High nutrient concentrations favour, to a certain extent, large phytoplankton species.

It was found by statistical analysis of modelling results with many different models (J0rgensen and Mejer, 1977; J0rgensen, 1992a, 1994), that there is a correlation between exergy and the buffer capacities; see Section 6.4. Some buffer capacities may be reduced even when the exergy increases, as mentioned above for the eutrophication case, but it is more than compensated by the increase of other buffer capacities. These results are consistent with the relation that exergy measures the energy needed to decompose the system to inorganic components (Svirezhev, 1992).

The above observations explain why it has been very difficult to find a relationship between ecosystem stabilities in the broadest sense and species diversity, as already discussed a few times. Stability of ecosystems in its broadest ecological sense should be considered as a multi-dimensional concept, and the relation between species diversity and stability is therefore not simple and can be only revealed by a multi-dimensional relation. If species diversity decreases, the stability (represented by buffer capacities) may decrease in some directions, but will increase in others. It may be formulated as the following: if the system can offer a better survival, i.e. bigger buffer capacities in relation to the changing forcing functions by decreasing the diversity, the system will not hesitate to react accordingly. See also Chapters 6 and 9.

The above-mentioned relation between exergy and buffer capacities indicates that point 4 in the definition of ecosystem integrity is globally covered by the use of exergy as ecological indicator, but because there is almost an infinite number of buffer capacities, and it would therefore be impossible to cover them all, this relationship between exergy and buffer capacities can only be applied semi-quantitatively in practice. As the concepts of ecosystem stability, resilience and ecosystem integrity are multi-dimensional, it will often be necessary to supplement the computations of exergy by relevant and focal buffer capacities. Buffer capacities related to the management situation should be selected. If we are concerned with the influence of toxic substances, the buffer capacities based upon the changes provoked by the input of toxic substances should be selected. If we are concerned with acid rain and its influence on the forest, we should find the buffer capacities relating the pH of rain water to the growth of trees in the forest, and so on. The result will be a limited number of buffer capacities. To keep the ecosystem healthy, we should consider these focal buffer capacities in our environmental management strategies. As long as the buffer capacities can withstand the stress with only minor changes, the ecosystem should be considered healthy.

Costanza (1992) has proposed an overall system integrity index consisting of system vigour, system organisation and system resilience. System vigour and the global system resilience are in accordance with the above presentation described by using exergy. The organisation is better covered by the specific exergy as it is highly dependent on the species diversity and their organisation, and independent of the total biomass. As stability is multi-dimensional it would be an improvement in the assessment of ecosystem integrity to include focal buffer capacities related to actual or possible stress situations.

As pointed out by Costanza (1992) these concepts will require a heavy dose of systems modelling. It would be possible to assess the concentrations of the most important species or classes of species, and then calculate the exergy and the specific exergy, but it would require a dynamic model based upon mass balances to find the buffer capacities, as they relate changes in forcing functions with changes in state variables, unless it can be presumed that the relationships between forcing functions and state variables are linear. This does not imply that a new model has been developed for every new case study, because models have a certain generality and the experience from one modelling study to the next is essential. Furthermore, if the seasonal changes in exergy and specific exergy should be assessed, it will either require many measurements throughout the year or the development of a model that is able to simulate the seasonal changes. Exergy and specific exergy usually vary significantly during the year to reflect the ability of the ecosystem to cope with the changes in temperature, precipitation and other climatic factors. A model will, furthermore, have the advantage that it can answer questions such as: how will the ecosystem integrity change if the forcing functions are changed so and so?

These considerations lead to the following tentative procedure for a practical assessment of ecosystem integrity.

1. Set up relevant questions related to the integrity of a considered ecosystem.

2. Assess the most important mass flows and mass balances related to these questions.

3. Make a conceptual diagram of the ecosystem, containing the components of importance for the mass flows defined under 2.

4. Develop a dynamic model (if the data are not sufficient, a steady-state model should be applied) using the usual procedure (see, for instance, J0rgensen, 1994).

5. Calculate exergy, specific exergy and relevant buffer capacities by the use of the model. If the model is dynamic it will also be possible to find the seasonal changes in exergy, specific exergy and buffer capacities.

6. Assess the ecosystem integrity: high exergy, specific exergy and buffer capacities imply a good ecosystem integrity. If the exergy and specific exergy are high, but one of the focal buffer capacities is low, then the "medicine" is to improve the structure of the ecosystem to assure a higher focal buffer capacity. If the exergy is high, but the specific exergy and some focal buffer capacities are low, we would probably be dealing with a eutrophic system, where the "medicine" should be a reduction of the nutrient loadings. Based upon the values of the three indicators, different measures should be taken to improve the ecosystem integrity.

13.3. Assessment of ecosystem integrity. An example: a lake ecosystem

Given below is an example of the application of exergy, specific exergy and buffer capacity as indicators of ecosystem integrity (J0rgensen, 1994). The same approach has been applied to the models of wetlands, fishponds, streams and agricultural systems with the same general results. The case study should therefore be considered as an illustrative example. A eutrophication model with seven state variables has been applied: nutrients, phytoplankton, zooplankton, planktivorous fish, carnivorous fish, detritus and sediment. The usual equations (see, for instance, J0rgensen, 1976, 1986) are applied, but the following characteristics according to ecological observations have been introduced.

1. For grazing and predation the threshold concentrations are used, below which no grazing and predation take place.

2. The predation by the most carnivorous fish on the planktivorous fish is reduced above a certain concentration of phytoplankton to consider that carnivorous fish are hunting by sight.

3. The growth rate of phytoplankton and zooplankton are reduced step-wise from low nutrient concentrations to high nutrient concentrations in accordance with the observations that bigger species prevail at a higher level of eutrophication as discussed above.

4. Adaptation to changed temperature is used by changing the optimum temperature accordingly.

5. The flow rate relative to the volume is 0.1, which assures a fast reaction to the nutrient concentration in flowing water.

6. The model does not distinguish between phosphorus and nitrogen, but assumes that they are present in the ratio used by phytoplankton, i.e. 1:7. The photosynthesis follows the uptake of nutrient by a factor of 12, corresponding to 11 times as much uptake of carbon, hydrogen, oxygen and other elements than that of nitrogen and phosphorus.

The model computes the exergy and the specific exergy. The buffer capacities for changes in phytoplankton, zooplankton and the two classes of fish, when the inputs of nutrients and the temperature are changed, are found using a sensitivity analysis. A partial buffer capacity, fiik, can be estimated as kth forcing function/ith state variable. It is observed that a small change in a forcing function implies a change in a selected state variable. The ratio between the changes corresponds to the buffer capacity. A high buffer capacity means that the given component of the ecosystem is resistant against changes in the given forcing function. Changes are more easily controlled. There are, of course, many buffer capacities corresponding to many combinations of forcing function and state variables.

Figs. 13.1-13.3 show some of the results. Exergy, specific (or sometimes also called structural) exergy and buffer capacity of phytoplankton to changed nutrients loading are plotted versus the nutrient concentration in flowing water. As seen the exergy increases with the increased nutrient input due to the resulting higher total biomass concentration. Specific exergy has a maximum at the nutrient concentration about 2 mg/l. With higher nutrient inputs, the specific exergy declines due to an unequal distribution of the biomass. Particularly the phytoplankton and the planktivorous fish increase on behalf of zooplankton and carnivorous fish. A structural change is observed, which is consistent with general observations in lakes; see also the results presented in Figs. 13.1 and 13.3. The buffer capacity of phytoplankton to changed nutrient loading has a minimum at a total nutrient input of about 2. It increases as discussed above with the increased nutrient loading mainly due to the slower growth rate.

Other changes in buffer capacities can be summarised as follows.

1. The buffer capacity for the influence of nutrients on the carnivorous fish is increasing with increasing nutrient loading. After a certain nutrient input the concentrations of carnivorous fish remain low at almost the same level independent of the nutrient concentration.


Fig. 13.1. The results obtained by the use of a eutrophication model with seven state variables are shown. The exergy is plotted versus the total inputs of nutrients (nitrogen and phosphorus, mg/l). The curve reflects the increase in biomass, which grows slower than linear with the nutrient concentration.


Fig. 13.1. The results obtained by the use of a eutrophication model with seven state variables are shown. The exergy is plotted versus the total inputs of nutrients (nitrogen and phosphorus, mg/l). The curve reflects the increase in biomass, which grows slower than linear with the nutrient concentration.

Specific exergy (TJ/g) versus nutrients (mg/l)

Specific exergy (TJ/g) versus nutrients (mg/l)

Fig. 13.2. The results obtained from the eutrophication model with seven state variables are shown. The specific exergy is plotted versus the total inputs of nutrients (nitrogen and phosphorus).


Fig. 13.2. The results obtained from the eutrophication model with seven state variables are shown. The specific exergy is plotted versus the total inputs of nutrients (nitrogen and phosphorus).

Towards a Thermodynamic Theory for Ecological Systems Buffer capacity phytoplankton relative nutrients input

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